System and method for signal limiting

ABSTRACT

A method for processing a signal with a corresponding noise profile includes analyzing spectral content of the noise profile, filtering at least one noise harmonic within the signal based on the analyzed spectral content, and limiting the filtered signal. The noise profile may include a phase noise profile. The signal may include a sinusoidal signal and/or a noise signal. At least one filter coefficient that is used to filter the at least one noise harmonic may be determined. The filtering may include low pass filtering. The limiting may include hard-limiting of the filtered signal. A phase difference between the limited signal and a reference signal may be detected.

RELATED APPLICATIONS

The present application is a continuation-in-part of application Ser.No. 09/634,552, filed Aug. 8, 2000 which claims benefit from andpriority to Application No. 60/160,806, filed Oct. 21, 1999; ApplicationNo. 60/163,487, filed Nov. 4, 1999; Application No. 60/163,398, filedNov. 4, 1999; Application No. 60/164,442, filed Nov. 9, 1999;Application No. 60/164,194, filed Nov. 9, 1999; Application No.60/164,314, filed Nov. 9, 1999; Application No. 60/165,234, filed Nov.11, 1999; Application No. 60/165,239, filed Nov. 11, 1999; ApplicationNo. 60/165,356; filed Nov. 12, 1999; Application No. 60/165,355, filedNov. 12, 1999; Application No. 60/172,348, filed Dec. 16, 1999;Application No. 60/201,335, filed May 2, 2000; Application No.60/201,157, filed May 2, 2000; Application No. 60/201,179, filed May 2,2000; Application No. 60/202,997, filed May 10, 2000; Application No.60/201,330, filed May 2, 2000. The above referenced applications arehereby incorporated herein by reference in their entirety.

The present application is also a continuation-in-part of U.S. patentapplication Ser. No. 10/409,213, filed Apr. 3, 2003 and entitled “PhaseLocked Loop That Avoids False Locking,” the complete subject matter ofwhich is hereby incorporated herein by reference in its entirety.

The present application is related to U.S. patent application Ser. No.10/813,486, filed Mar. 30, 2004 and entitled System And Method ForReducing Phase Noise,” the complete subject matter of which is herebyincorporated herein by reference in its entirety.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[Not Applicable]

MICROFICHE/COPYRIGHT REFERENCE

[Not Applicable]

BACKGROUND OF THE INVENTION

Spectral purity and reduced phase noise are becoming an inseparablerequirement of signal generation and amplification circuits. Most moderncommunication systems, in particular, employ phase-locked loops (PLLs)and frequency synthesizers, along with their associated specifiedperformance. Those specifications normally dictate the performance ofindividual blocks, including voltage controlled oscillators (VCOs),dividers, etc. Traditionally, the noise and spectral profile ofdifferent blocks are included in a linear, phase domain AC-typeanalysis, or simulation, to estimate the final spectral performance of aPLL. Such analysis, however, ignores the nonlinear effects in the signalgeneration path, including a limiting action by a limiter, for example.

Limiters may be utilized with an electric circuit to transform asinusoidal wave into a square wave, for example. Because of thenon-linear effect in the signal generation path within the electriccircuit and the resulting phase noise profile, as outlined below, alimiting action by a limiter may substantially increase the phase noiseprofile of the generated signal at the output of the limiter.

Further limitations and disadvantages of conventional and traditionalapproaches will become apparent to one of skill in the art, throughcomparison of such systems with the present invention as set forth inthe remainder of the present application with reference to the drawings.

BRIEF SUMMARY OF THE INVENTION

Aspects of the present invention may be found in a method and system forprocessing a signal with a corresponding noise profile. Aspects of themethod may comprise analyzing spectral content of the noise profile. Atleast one noise harmonic within the signal may be filtered based on saidanalyzed spectral content. The filtered signal may be limited. The noiseprofile may comprise a phase noise profile. The signal may comprise atleast one of a sinusoidal signal and a noise signal. At least one filtercoefficient that is used to filter the at least one noise harmonic maybe determined. The filtering may comprise low pass filtering and thelimiting may comprise hard-limiting the filtered signal. The signal maybe modulated prior to the filtering.

The signal may be downconverted prior to the modulating. At least onesignal component of the signal may be downconverted. The at least onesignal component of the signal may comprise an in-phase signal componentand a quadrature signal component. The downconverted signal may be mixedwith a local oscillator signal. The mixed signal may be filtered. Thefiltering may comprise low pass filtering of a sum of a carrierfrequency of the signal and a reference frequency of the localoscillator signal. The in-phase signal component and the quadraturesignal component may be modulated with a modulation frequency. Themodulated in-phase signal component and the modulated quadrature signalcomponent may be added to obtain a downconverted modulated signal. Aphase difference may be detected between the limited signal and areference signal.

Aspects of the system may comprise a processor that analyzes spectralcontent of the noise profile. A filter may filter at least one noiseharmonic within the signal based on the analyzed spectral content. Alimiter may limit the filtered signal. The noise profile may comprise aphase noise profile and the signal may comprise at least one of asinusoidal signal and a noise signal. The processor may determine atleast one filter coefficient that is used to filter the at least onenoise harmonic. The filter may comprise a low-pass filter and thelimiter may comprise a hard-limiter that limits the filtered signal. Amodulator may modulate the signal prior to the filtering. Adownconverter may downconvert the signal prior to the modulating. Morespecifically, the downconverter may downconvert at least one signalcomponent of the signal.

The at least one signal component of the signal may comprise an in-phasesignal component and a quadrature signal component. A mixer may mix thedownconverted signal with a local oscillator signal. A filter may filterthe mixed signal. The filter may comprise a low pass filter that filtersa sum of a carrier frequency of the signal and a reference frequency ofthe local oscillator signal. A modulation mixer may modulate thein-phase signal component and the quadrature signal component with amodulation frequency. An adder may add the modulated in-phase signalcomponent and the modulated quadrature signal component to obtain adownconverted modulated signal. A phase detector may detect a phasedifference between the limited signal and a reference signal.

These and other features and advantages of the present invention may beappreciated from a review of the following detailed description of thepresent invention, along with the accompanying figures in which likereference numerals refer to like parts throughout.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 is a graphical representation of power spectral density (PSD) fora noise-containing sinusoidal signal, in accordance with an embodimentof the invention.

FIG. 2 is a graphical representation of the modulating phase of thesinusoidal signal of FIG. 1, in accordance with an embodiment of theinvention.

FIG. 3 is a graphical representation of phase modulation and amplitudemodulation of a sinusoidal signal passed through a limiter, inaccordance with an embodiment of the invention.

FIG. 4 is a schematic block diagram of a limiter, in accordance with anembodiment of the invention.

FIG. 5 is a graphical representation of output voltage components andoutput voltage of the limiter in FIG. 4, in accordance with anembodiment of the invention.

FIG. 6 is a graphical representation of noise profile and voltage for aninput signal of the limiter in FIG. 4, in accordance with an embodimentof the invention.

FIG. 7 is a graphical representation of a large sinusoidal signal and asmall sinusoidal signal applied to a limiter, in accordance with anembodiment of the invention.

FIG. 8 is a graphical representation of a soft limiter, in accordancewith an embodiment of the invention.

FIG. 9 is a graphical representation of output voltage for the limiterin FIG. 8, in accordance with an embodiment of the invention.

FIG. 10 is a graphical representation of a noise component for theoutput voltage of FIG. 9, in accordance with an embodiment of theinvention.

FIG. 11 is a graphical representation in frequency domain of the outputvoltage of FIG. 9, in accordance with an embodiment of the invention.

FIG. 12 is a graphical representation of perturbation spectrum of outputvoltage component of the output voltage of FIG. 9, in accordance with anembodiment of the invention.

FIG. 13 is a graphical representation in frequency domain of outputvoltage from a limiter with a single side band perturbation in the inputsignal, in accordance with an embodiment of the invention.

FIG. 14 is a graphical representation in frequency domain of input andoutput voltage from a limiter with a single side band perturbation in asinusoid input signal, in accordance with an embodiment of theinvention.

FIG. 15 is a graphical representation in frequency domain of a samplingfunction component within output voltage from a limiter, in accordancewith an embodiment of the invention.

FIG. 16 is a graphical representation in frequency domain of input andoutput voltage from a limiter with a single side band perturbation in acosine input signal, in accordance with an embodiment of the invention.

FIG. 17 is a graphical representation in frequency domain of oscillationinput with PM and output voltage from a limiter, in accordance with anembodiment of the invention.

FIG. 18 is a graphical representation in frequency domain of powerspectral density of a limiter input of a large sinusoid with a randomprocess and a limiter output, in accordance with an embodiment of theinvention.

FIG. 19 is a graphical representation of power spectral density of phasenoise of a voltage controlled oscillator, in accordance with anembodiment of the invention.

FIG. 20 is a schematic block diagram of a voltage controlled oscillatorthat may be utilized in accordance with an embodiment of the invention.

FIG. 21 is a schematic block diagram of a binary phase shift keying(PSK) modulator utilizing a limiter and a filter, in accordance with anembodiment of the invention.

FIG. 22 is a graphical representation of an exemplary signal noisecharacteristic for a limited signal with filtration, in accordance withan embodiment of the invention.

FIG. 23 is a graphical representation of an exemplary signal noisecharacteristic for a limited signal without filtration, in accordancewith an embodiment of the invention.

FIG. 24 is a flow diagram of an exemplary method for processing asinusoidal wave signal with a phase noise profile, in accordance with anembodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Nonlinear operations within an electric circuit, such as limiting, maycause distortion and aliasing in the signal and noise spectrum. Inparticular, it may be established for a hard-limiter, for example, thata limiting action by the hard-limiter may cause infinite folding andgeneration of harmonics at the output of the signal limiter.

In accordance with an aspect of the invention, certain techniquesrelating to the effect of non-linearity on phase noise profile andsignal, which are illustrated below, may be utilized to predict thebehavior of an electric signal as it traverses through a circuitcomprising a limiter. It may be established that if the limiter gain isnot infinite, the close-in phase noise may change depending on how sharpthe limiter transitions are. In addition, these derivations may beutilized to predict the spectral properties of a signal within a circuitcontaining a limiter.

In another aspect of the invention, the phase noise profile of asinusoidal signal within an electric circuit may be determined, prior toa limiting action by a limiter within the circuit. For example, spectralanalysis may be utilized to analyze the spectral content of a noiseprofile of a given signal. One or more filter coefficients of a filtermay then be generated based on the analyzed spectral content. The signalmay then be filtered in accordance with the determined filtercoefficients so that one or more phase noise characteristics, orperturbations, may be attenuated from the signal. In this way, after thefiltered signal passes through a limiter, the infinite folding andgeneration of noise harmonics at the limiter output may be avoided.

The output of a signal generation circuit, such as a voltage controlledoscillator (VCO), may be represented by:

x(t)=A(t)cos(2πf _(c) t+φ(t))  (1)

For an ideally sinusoidal signal source, A(t) may be equal to a constantA₀, and φ(t) may be constant or equal to zero. If the signal phasevaries with time in a sinusoidal fashion, the output of the signalgeneration circuit may be represented by:

x(t)=A ₀ cos(2πf _(c) t+m sin 2πf _(m) t)  (2)

Utilizing frequency modulation (FM) theory, expression (2) may befurther expanded in terms of modified Bessel functions. In this way,sinusoidal modulation of the phase may result in generation of sidebandsat integer multiples of modulation frequency f_(m) with respect to thecenter frequency f_(c). If m is smaller than 1, the following smallmodulation index approximation may be inferred:

$\begin{matrix}{{x(t)} \approx {{A_{0}\cos \; 2\pi \; f_{c}t} + {A_{0}{\frac{m}{2}\left\lbrack {{\cos \; 2{\pi \left( {f_{c} + f_{m}} \right)}t} - {\cos \; 2{\pi \left( {f_{c} - f_{m}} \right)}t}} \right\rbrack}}}} & (3)\end{matrix}$

FIG. 1 is a graphical representation 100 of power spectral density (PSD)for a noise-containing sinusoidal signal, in accordance with anembodiment of the invention. PSD may be undefined for a deterministicsignal. However, a deterministic signal may be assumed to contain asmall and negligible random process, such as noise. In this case, thePSD may be well defined. Referring to FIG. 1, the random noise may bereflected in frequency domain at frequencies 101, 103, 105, and 107,disposed around the mirror center frequency −f_(c) 109 and f_(c) 111.

FIG. 2 is a graphical representation 200 of the modulating phase of thesinusoidal signal of FIG. 1, in accordance with an embodiment of theinvention. Referring to FIG. 2, there is illustrated a PSD 203 of amodulating phase f_(m) 201. In the signal PSD, the phase PSD may bereplicated around a carrier frequency f_(c).

In a more general case:

x(t)=(A ₀ +a(t))·cos(2πf _(c) t+m sin 2πf _(m) t)  (4)

Through the small modulation index approximation and the assumption thata(t)<<A₀, equation (4) may be simplified to:

$\begin{matrix}{{x(t)} \approx {{A_{0}\cos \; 2\pi \; f_{c}t} + {{a(t)}\cos \; 2\pi \; f_{c}t} + {A_{0}{\frac{m}{2}\left\lbrack {{\cos \; 2{\pi \left( {f_{c} + f_{m}} \right)}t} - {\cos \; 2{\pi \left( {f_{c} - f_{m}} \right)}t}} \right\rbrack}}}} & (5)\end{matrix}$

In particular, for a(t)=a₀ cos 2πf_(m)t:

$\begin{matrix}{{x(t)} = {{A_{0}\cos \; 2\pi \; f_{c}t} + {\left( {\frac{a_{0}}{2} + {A_{0}\frac{m}{2}}} \right)\cos \; 2{\pi \left( {f_{c} + f_{m}} \right)}t} + {\left( {\frac{a_{0}}{2} - {A_{0}\frac{m}{2}}} \right)\cos \; 2{\pi \left( {f_{c} - f_{m}} \right)}t}}} & (6)\end{matrix}$

The sidebands created at the modulation frequency f_(m) may be caused byamplitude modulation (AM) and/or phase modulation (PM). For smallvariations, AM and PM may be indistinguishable.

FIG. 3 is a graphical representation 300 of phase modulation andamplitude modulation of a sinusoidal signal passed through a limiter, inaccordance with an embodiment of the invention. If a large sinusoidalwave is accompanied by a small one, it may be determined:

x(t)=A ₀ cos 2πƒ_(c) t+A ₂ cos 2πƒ₂ t A₀>>A₂  (7)

Equation (7) may be rearranged to yield:

$\begin{matrix}{{x(t)} = {{A_{0}\cos \; 2\pi \; f_{c}t} + {\left( {\frac{A_{2}}{2} + {A_{0}\frac{A_{2}}{2A_{0}}}} \right){\cos\left\lbrack {{2{\pi\left( {f_{c} + \left( {f_{2} - f_{c}} \right)} \right\rbrack}t} + {\left( {\frac{A_{2}}{2} - {A_{0}\frac{A_{2}}{2A_{0}}}} \right){\cos\left\lbrack {2{\pi\left( {f_{c} - \left( {f_{2} - f_{c}} \right)} \right\rbrack}t} \right.}}} \right.}}}} & (8)\end{matrix}$

Utilizing equation (6), equation (8) may be represented as a sinusoidalwave with amplitude and phase modulation:

$\begin{matrix}{{{x(t)} = {\left( {A_{0} + {a_{0}\cos \; 2\pi \; f_{m}t}} \right) \cdot {\cos \left( {{2\pi \; f_{c}t} + {m\; \sin \; 2\pi \; f_{m}t}} \right)}}},{a_{0} = A_{2}},{m = \frac{A_{2}}{A_{0}}},{f_{m} = {f_{2} - f_{c}}}} & (9)\end{matrix}$

If the amplitude modulation is suppressed, for example by passing thesignal through a circuit, such as a limiter, which reacts to zerocrossings, for example, the result may be a sinusoidal wave with phasemodulation only. In this way, the passing of the signal through acircuit may result in two side bands:

$\begin{matrix}{{y(t)} = {{A_{0}\cos \; 2\pi \; f_{c}t} + {\frac{A_{2}}{2}\cos \; 2{\pi \left( {f_{c} + f_{m}} \right)}t} - {\frac{A_{2}}{2}\cos \; 2{\pi \left( {f_{c} - f_{m}} \right)}t}}} & (10)\end{matrix}$

Referring to FIG. 3, graphical representation 301 may illustrate alimiter input signal X(f) in frequency domain. The signal X(f) maycomprise a carrier signal at a center frequency f_(c) 314 and smallersinusoidal signal at frequency f₂ 313. The mirror images of the centerfrequency f_(c) and the sinusoidal signal at frequency f₂ may be locatedat frequencies −f_(c) 312 and −f₂ 311.

The graphical representation 303 may illustrate decomposition of thesmall sinusoid within the signal X(f) into AM and PM components. Forexample, the small sinusoid at frequency f₂ 313 may be decomposed intoAM components at frequencies 323 and 327, and PM components atfrequencies 325 and 329. Similarly, the mirror image −f₂ 311 may bedecomposed into AM components at frequencies 317 and 319, and PMcomponents at frequencies 315 and 321.

The graphical representation 305 may represent, for example, AM to PMconversion within an exemplary output signal Y(f) of a limiter when aninput signal X(f) is applied to it. As a result, the AM sidebands may besuppressed and two PM sidebands, at frequencies 335 and 337, may remain.PM sidebands 331 and 333 may correspond to sidebands 337 and 335,respectively.

In order to obtain the spectrum at the output of a limiter in terms ofits input, a limiter may be considered as a high-gain amplifier. FIG. 4is a schematic block diagram 400 of a limiter, in accordance with anembodiment of the invention. Referring to FIG. 4, the limiter 409 maylimit an input signal 405 to generate an output signal 407. The inputsignal 405 may comprise two sinusoidal signals 401 and 403 with equalamplitudes. The limiter output 407 may be represented by the timingdiagram 411. In this way, the limiter output 407 may switch between anegative and a positive level, −V_(m) and V_(m) respectively, dependingon weather the input is smaller or larger than zero. The input to thelimiter may be represented by:

V _(in)(t)=A sin(2πƒ₁ t)+A sin(2πƒ₂ t+θ)  (11)

Since the limiter 409 may only respond to the zero crossings of V_(in),the amplitude A is irrelevant and only the relative amplitude of the twosinusoidal waves 401 and 403 may be considered. Zero crossings occur atV_(in)=0:

sin(2πƒ₁ t)=sin(−2πƒ₂ t−θ)  (12)

Two sets of answers satisfy this condition.

$\begin{matrix}\left\{ {\begin{matrix}{{2\pi \; f_{1}t} = {{{- 2}\pi \; f_{2}t} - \theta + {2k\; \pi}}} \\{{2\pi \; f_{1}t} = {\pi + {2\pi \; f_{2}t} + \theta + {2k\; \pi}}}\end{matrix}->\left\{ \begin{matrix}{{2{\pi \left( {f_{1} + f_{2}} \right)}t} = {{2k\; \pi} - \theta}} \\{{2{\pi \left( {f_{1} - f_{2}} \right)}t} = {{2k\; \pi} + \pi + \theta}}\end{matrix} \right.} \right. & (13)\end{matrix}$

Therefore, the times at which zero crossing may happen are:

$\begin{matrix}\left\{ \begin{matrix}{t = {{\frac{1}{f_{1} + f_{2}}\left( {k - \frac{\theta}{2\pi}} \right)} = {\frac{1}{f_{+}}\left( {k - \frac{\theta}{2\pi}} \right)}}} \\{t = {{\frac{1}{f_{1} - f_{2}}\left( {k + \frac{\theta + \pi}{2\pi}} \right)} = {\frac{1}{f_{-}}\left( {k + \frac{\theta + \pi}{2\pi}} \right)}}}\end{matrix} \right. & (14)\end{matrix}$

This means that the output crosses zero at any of these times. Theoutput may be considered as a product of two square waves, one with afrequency of f⁻/2, and the other with a frequency of f₊/2, eachrepresenting one of the two sets of solutions:

V _(out)(t)=V _(m)×(V _(out+)(t)×V _(out−)(t))  (15)

In frequency domain:

V _(out)(ƒ)=V _(m)×(V _(out+)(ƒ)*V _(out−)(ƒ))  (16)

In the above equation (16), “*” denotes convolution.

FIG. 5 is a graphical representation 500 of output voltage componentsand output voltage of the limiter in FIG. 4, in accordance with anembodiment of the invention. Referring to FIG. 5, for the case of θ=0,the output voltage components V_(out+) and V_(out−) may be representedby the graphical representations 501 and 503, respectively. The outputvoltage components V_(out+) and V_(out−) in frequency domain may berepresented by the graphical representations 505 and 507, respectively.The total output voltage component V_(out) may be represented infrequency domain by the graphical representation 509.

Convolution of each impulse in the V_(out+) spectrum with V_(out−) maycreate a replica of the entire V_(out−) spectrum around that impulse.Thus, the general shape of the spectrum of V_(out) is a set of replicasof V_(out−) spectrum, spaced by odd multiples of f₊/2=(f₁+f₂)/2. Theoverlap of the replicas may or may not be substantial depending on therelative difference between f₁ and f₂. The overlap is not shown here forclarity. The spectrum may scale linearly with V_(m). In addition, theremay be smaller impulses repeated at multiples of f⁻ from the twoimpulses at f₁ and f₂. A similar pattern may occur at 3f₊/2, 5f₊/2, etc.It may be noticed from the graphical representation 500 that of thetotal output power of V_(m) ², approximately one third may go into eachof the two fundamental frequencies f₁ and f₂. In one aspect of theinvention, the above convolution equation for obtaining V_(out) may beutilized to predict phase noise harmonics, for example, within asinusoidal signal with a phase noise profile.

FIG. 6 is a graphical representation 600 of noise profile and voltagefor an input signal of the limiter in FIG. 4, in accordance with anembodiment of the invention. Referring to FIG. 6, an input signal V_(in)may comprise a large signal 601, or a carrier, with a mirror image 605,and a small signal 603 with a mirror image 607. The small signal 603 maycomprise a small sinusoidal wave:

V _(in)(t)=A ₁ sin(2πƒ₁ t)+A ₂ sin(2πƒ₂ t+θ)  (17)

The small sinusoid 603 may be regarded as noise, which may berepresented by V_(P)(t):

V _(in) =A ₁ sin(2πƒ₁ t)+V _(P)(t)  (18)

FIG. 7 is a graphical representation of a large sinusoid signal and asmall sinusoidal signal applied to a limiter, in accordance with anembodiment of the invention. Referring to FIG. 7, the large sinusoidalsignal 701 may have a zero crossing at point A. The perturbation 703 maymove the zero crossing of the sinusoidal signal 701 from point A topoint B. In order to obtain the spectrum of the output of a limiter, thelimiter may be approximated as a high gain amplifier that saturates atthe positive and negative supply levels, or as a soft limiter.

FIG. 8 is a graphical representation 800 of a soft limiter, inaccordance with an embodiment of the invention. If a pure sinusoidalwave were applied to the high gain amplifier, the output may beapproximated to a square wave, with flat sections 801 and 803. Duringtransitions, the output would be an amplified version of the input, witha gain of A, which is the slope 805.

FIG. 9 is a graphical representation 900 of output voltage for thelimiter in FIG. 8, in accordance with an embodiment of the invention.Referring to FIG. 9, graphical representation 901 illustrates the inputsignal, which may comprise a sinusoidal wave plus a small perturbation.The output signal V_(out) may be illustrated by the graphicalrepresentation 903. The output signal V_(out) may be decomposed intocomponents V_(out1) and V_(out2), such that V_(out)=V_(out1)+V_(out2),as illustrated on graphical representation 900. The transition time Δmay be obtained from:

$\begin{matrix}{{A_{1}{{\sin \left( {2\pi \; f_{1}\frac{\Delta}{2}} \right)} \cdot A}} = V_{m}} & (19) \\{\Delta = {\frac{1}{\pi \; f_{1}}{\sin^{- 1}\left( \frac{V_{m}}{{AA}_{1}} \right)}}} & (20)\end{matrix}$

For small Δ, or for Δ

1/πƒ₁:

$\begin{matrix}{\Delta \approx {\frac{1}{\pi \; f_{1}} \cdot \frac{V_{m}}{{AA}_{1}}}} & (21)\end{matrix}$

V_(out2) may be represented by the graph 907 as a chopped version of thesmall input perturbation, multiplied by A.

FIG. 10 is a graphical representation 1000 of a noise component for theoutput voltage of FIG. 9, in accordance with an embodiment of theinvention. Referring to FIG. 10, the output voltage component V_(out2)may be further decomposed into the product of V_(P)(t) and a samplingfunction V_(S)(t). Therefore, the output voltage may be presented as:

V _(out)(t)=V _(out1)(t)+V _(out2)(t)=V _(out1)(t)+V _(P)(t)×V_(S)(t)  (22)

V _(out)(ƒ)=V _(out1)(ƒ)+V _(P)(ƒ)*V _(S)(ƒ)  (23)

FIG. 11 is a graphical representation 1100 in frequency domain of theoutput voltage of FIG. 9, in accordance with an embodiment of theinvention. Referring to FIG. 11, the output voltage V_(out) may berepresented as the sum of two components—1101 and 1102. The firstcomponent 1101 may be represented by a periodic signal with thefundamental frequency of f=f₁. This signal may represent what the outputwould look like in the absence of any small perturbation at the input. AFourier transform of this signal may comprise impulses at odd harmonicsof f₁. The second component 1102 may be a sampled version of the smallperturbation, at a sampling frequency equal to 2f₁.

In this way, the output spectrum may be broken down as follows:

$\begin{matrix}{{V_{{out}\; 1}(f)} = {\sum\limits_{k = {- \infty}}^{\infty}{a_{k}{\delta \left( {f - {kf}_{1}} \right)}}}} & (24) \\{a_{k} = \left\{ \begin{matrix}0 & {{{if}\mspace{14mu} k} = {even}} \\{\frac{1}{2j} \cdot \left( {{2\; f_{1}{{AA}_{1}\left( {\Delta - \frac{\sin \left( {2\pi \; f_{1}\Delta} \right)}{2\pi \; f_{1}}} \right)}} + {\frac{4V_{m}}{\pi}{\cos \left( {\pi \; f_{1}\Delta} \right)}}} \right)} & {{{if}\mspace{14mu} k} = 1} \\{\frac{1}{2j} \cdot \left( {2f_{1}{{AA}_{1}\left( {\frac{\sin \left( {\left( {k - 1} \right)\pi \; f_{1}\Delta} \right)}{\left( {k - 1} \right)\pi \; f_{1}} - \frac{\sin \left( {\left( {k + 1} \right)\pi \; f_{1}\Delta} \right)}{\left( {k + 1} \right)\pi \; f_{1}} + {\frac{4V_{m}}{\pi \; k}{\cos \left( {k\; \pi \; f_{1}\Delta} \right)}}} \right)}} \right.} & {otherwise}\end{matrix} \right.} & (25)\end{matrix}$

For a small Δ, equation 125 may be simplified to:

$\begin{matrix}{a_{k} = {{\frac{1}{2j} \cdot \frac{1}{k} \cdot \frac{4V_{m}}{\pi}}\mspace{14mu} \left( {{odd}\mspace{14mu} k} \right)}} & (26)\end{matrix}$

Equation (26) may be a very close approximation as a a_(k)(Δ) is flataround Δ=0, when

${\frac{\partial a_{k}}{\partial\Delta}_{\Delta = 0}} = 0.$

Similarly,

$\begin{matrix}{{V_{S}(f)} = {\sum\limits_{k = {- \infty}}^{\infty}{b_{k}{\delta \left( {f - {k\left( {2f_{1}} \right)}} \right)}}}} & (27) \\{b_{0} = {{2A\; f_{1}\Delta \mspace{14mu} {and}\mspace{14mu} b_{k}} = {\frac{A}{k\; \pi}{\sin \left( {2k\; \pi \; f_{1}\Delta} \right)}\mspace{14mu} \left( {k > 0} \right)}}} & (28)\end{matrix}$

As the limiter becomes more ideal and A→∞ and Δ→0, V_(S)(t) may turninto an impulse train, for which:

$\begin{matrix}{{b_{k} \approx {\frac{A}{k\; \pi}2k\; \pi \; f_{1}\Delta}} = {2{Af}_{1}\Delta}} & (29)\end{matrix}$

For a small Δ:

$\begin{matrix}{{b_{k} \approx {2A\; {f_{1} \cdot \frac{1}{\pi \; f_{1}} \cdot \frac{V_{m}}{{AA}_{1}}}}} = \frac{2V_{m}}{\pi \; A_{1}}} & (30)\end{matrix}$

FIG. 12 is a graphical representation 1200 of perturbation spectrum ofoutput voltage component of the output voltage of FIG. 9, in accordancewith an embodiment of the invention. Referring to FIG. 12, the outputvoltage component V_(out2)(f) may comprise replicas of the input smallperturbation spectrum 1201 repeated every 2f₁. The replicas may bescaled by 2V_(m)/(πA₁), and they may also be folded onto each other. Theoutput voltage may be presented as:

$\begin{matrix}{{V_{out}(f)} = {{\sum\limits_{k = {odd}}{a_{k}{\delta \left( {f - {kf}_{1}} \right)}}} + {{V_{P}(f)}*{\sum\limits_{k = {- \infty}}^{\infty}{b_{k}{\delta \left( {f - {k\left( {2f_{1}} \right)}} \right)}}}}}} & (31) \\{{V_{out}(f)} = {{\sum\limits_{k = {odd}}{a_{k}{\delta \left( {f - {kf}_{1}} \right)}}} + {\sum\limits_{k = {- \infty}}^{\infty}{b_{k}{V_{P}\left( {f - {k\left( {2f_{1}} \right)}} \right)}}}}} & (32)\end{matrix}$

FIG. 13 is a graphical representation 1300 in frequency domain of outputvoltage from a limiter with a single side band perturbation in the inputsignal, in accordance with an embodiment of the invention. Referring toFIG. 13, the output voltage may be represented by:

$\begin{matrix}{{V_{out}(f)} = {{\sum\limits_{k = {odd}}{\frac{4V_{m}}{2j\; k\; \pi}{\delta \left( {f - {kf}_{1}} \right)}}} + {\frac{2V_{m}}{\pi \; A_{1}}{\sum\limits_{k = {- \infty}}^{\infty}{V_{P}\left( {f - {k\left( {2f_{1}} \right)}} \right)}}}}} & (33)\end{matrix}$

With regard to passing a signal with phase noise profile through alimiter, the output of the limiter may be represented as the sum of twocomponents. The first part may comprise a square wave at f=f₁, which iswhat the output spectrum would be in the absence of any smallperturbation. The second part may comprise a sampled version of thesmall perturbation, at a sampling frequency equal to 2f₁. Because of thesampling action, the mirrored spectrum of the perturbation may fold ontop of itself, around the odd multiples of the carrier frequency.

In this way, a single sideband perturbation (SSB) may occupy only onesingle sideband of the carrier as there is energy only on one side ofthe carrier and its total bandwidth is smaller than f₁. Consequently, ifthe carrier to SSB ratio at the input is:

$\begin{matrix}{{R_{input} = \frac{A_{1}/2}{\alpha}},} & (34)\end{matrix}$

then at the output, the ratio of carrier to each SSB becomes:

$\begin{matrix}{{R_{output} = {\frac{\frac{V_{m}}{2\pi}}{\frac{2V_{m}}{\pi \; A_{1}}\alpha} = {2R_{input}}}},} & (35)\end{matrix}$

as illustrated on FIG. 13. Therefore, the carrier to each sideband ratiomay be reduced but with a resulting increase in the sidebands.

FIG. 14 is a graphical representation 1400 in frequency domain of inputand output voltage from a limiter with a single side band perturbationin a sinusoid input signal, in accordance with an embodiment of theinvention. Referring to FIG. 14, the input signal 1403 may comprise asum of one large sinusoidal wave 1401 and one small sinusoidal wave1402. At the input, the carrier frequency may be at f=f₁, the singlesideband may be at f=f₂, and the carrier to sideband ratio may be A₁/A₂.At the output, the sideband 1402 may be split into two smaller sidebands1407, at f=f₂, and 1405, at f=2f₂−f₁. The carrier to sideband ratio foreach sideband may be (A₁/A₂)/2. In this way, the additive AM may beconverted into PM sidebands, as indicated earlier. Analyticalexpressions may be derived if A is not large, using the formulas fora_(n) and b_(n) coefficients in V_(out1)(f) and V_(S)(f).

FIG. 15 is a graphical representation 1500 in frequency domain of asampling function component within output voltage from a limiter, inaccordance with an embodiment of the invention. Referring to FIG. 15, ifA is finite and, therefore, Δ is non-zero, the sampling signal V_(S)(t)1501 may comprise a series of diminishing impulses in frequency domainwith a sinc-shape envelope. The impulses may be spaced by 2f₁ and thesinc zeros may be at multiples of 1/Δ. If the zeros of the sinc coincidewith the impulses, when 2f₁=1/Δ and Δ=T₁/2, then V_(S)(f) may be reducedto a single impulse of magnitude A at f=0. Under these conditions,V_(out1)=0. The output voltage may then be presented as:

V _(out)(ƒ)=0+V _(in)(ƒ)*V _(x)(ƒ)=A·V _(in)(ƒ)  (36)

Such result may be expected since when Δ=T₁/2, the input waveform may besmall, so that the limiter may not saturate and may be always in itslinear regime. Therefore, the signal may be amplified with a gain of A.

FIG. 16 is a graphical representation 1600 in frequency domain of inputand output voltage from a limiter with a single side band perturbationin a cosine input signal, in accordance with an embodiment of theinvention. Referring to FIG. 16, the input signal 1601 may comprise acosine input signal with a single side band perturbation.

FIG. 17 is a graphical representation in frequency domain of oscillationinput with PM and output voltage from a limiter, in accordance with anembodiment of the invention. Referring to FIG. 17, the input signalV_(OSC) 1701 may comprise an oscillation with a small PM modulation incosine form, and may be represented by:

$\begin{matrix}{\mspace{79mu} {{V_{OSC}(t)} = {A_{0}{\cos \left( {{2\pi \; f_{c}t} + {m\; \sin \; 2\pi \; f_{m}t}} \right)}}}} & (37) \\{{V_{OSC}(t)} \approx {{A_{0}\cos \; 2\pi \; f_{c}t} + {A_{0}{\frac{m}{2}\left\lbrack {{\cos \; 2{\pi \left( {f_{c} + f_{m}} \right)}t} - {\cos \; 2{\pi \left( {f_{c} - f_{m}} \right)}t}} \right\rbrack}}}} & (38)\end{matrix}$

The output signal V_(out) 1703 may be obtained by utilizing theinformation in FIG. 16. For simplicity, it may be assumed, for example,that 4V_(m)/π=A₀, or the gain for the cosine wave at f_(c) is equal to1.

FIG. 18 is a graphical representation 1800 in frequency domain of powerspectral density of a limiter input of a large sinusoid with a randomprocess and a limiter output, in accordance with an embodiment of theinvention. Referring to FIG. 18, the random process n(t) 1801 may berepresented as noise, for example, with relatively small amplitude and agiven power spectral density S_(nn)(t). The PSD of the smallperturbation 1801 and its mirrored version 1803 may be repeated aroundodd multiples of the carrier. The parts of the PSD that fold on top ofeach other may not be randomly added up. In case of a Fourier transformof deterministic signals, when adding two spectrums, the phaseinformation may correctly sum the amplitudes. Similarly, to correctlyadd power spectral densities, information regarding their correlationmay be utilized. If two random processes x(t) and y(t) are added to forma random process z(t), the resulting PSD may be represented by:

$\begin{matrix}{\mspace{79mu} {{S_{ZZ}(f)} = {{F\left( {R_{ZZ}(\tau)} \right)} = {F\left( {E\left\lbrack {{z(t)} \cdot {z\left( {t + \tau} \right)}} \right\rbrack} \right)}}}} & (39) \\{\mspace{79mu} {{S_{ZZ}(f)} = {F\left( {E\left\lbrack {\left( {{x(t)} + {y(t)}} \right) \cdot \left( {{x\left( {t + \tau} \right)} + {y\left( {t + \tau} \right)}} \right)} \right\rbrack} \right)}}} & (40) \\{{S_{ZZ}(f)} = {F\left( {E\left\lbrack {\left( {{x(t)}{x\left( {t + \tau} \right)}} \right\rbrack + {E\left\lbrack {{y(t)}{y\left( {t + \tau} \right)}} \right\rbrack} + {E\left\lbrack {\left( {{x(t)}{y\left( {t + \tau} \right)}} \right\rbrack + {E\left\lbrack {{x\left( {t + \tau} \right)}{y(t)}} \right\rbrack}} \right)}} \right.} \right.}} & (41)\end{matrix}$

If the two processes x(t) and y(t) are uncorrelated, the last two termsin the Fourier transform may be reduced to zero:

S _(ZZ)(ƒ)=F(E[(x(t)x(t+τ)])+F(E[y(t)y(t+τ)])  (42)

S _(ZZ)(ƒ)=S _(XX)(ƒ)+S _(YY)(ƒ)  (43)

If the signals are correlated, the above equation may not hold. Inparticular, if y(t)=αx(t), then:

S _(ZZ)(ƒ)=(1+α)² S _(XX)(ƒ)  (44)

If two areas of the power spectrum which are 100% correlated, or theirunderlying random processes are the same and act in the same direction,fold onto each other, the resulting PSD may not double, but mayquadruple, according to the above formula.

If a large sinusoidal wave is accompanied by wideband thermal noise,according to FIG. 18, the thermal noise may fold on top of itself forevery convolution with the impulses in the sampling function. If thethermal noise is not bandlimited, it may fold on itself an infinitenumber of times. Since the areas that fold on each other areuncorrelated, the PSDs may add up directly and subsequently the resultmay become infinite.

Thermal noise, however, is mostly bandlimited. Thus, in the process ofhard-limiting, the noise may fold onto itself only a limited number oftimes. A limiter, therefore, may increase the thermal noise level if ithas a relatively wide band. It may be shown that if a large sinusoidalwave accompanied by a bandlimited thermal noise is passed through alimiter, the output PSD of noise on the left side, from f=0 to f=f_(c),and the right side, from f=f_(c) to f=2f_(c), of the carrier may becorrelated.

FIG. 19 is a graphical representation 1900 of power spectral density ofphase noise of a voltage controlled oscillator, in accordance with anembodiment of the invention. The output signal in a typical integratedVCO may be represented by:

x(t)=A cos(2πƒ₁ t+φ(t))  (45)

Where the term φ(t) may reflect the phase variation due to the noisesources in the VCO. Referring to FIG. 19, there is illustrated the powerspectral density of phase noise S_(φφ)(f). A VCO by definition is aphase integrator and, therefore, the power spectral density of the VCOoutput phase, in terms of the input modulating process, may berepresented by:

$\begin{matrix}{{{S_{\varphi\varphi}(f)} = {\frac{K_{V}^{2}}{f^{2}}{S_{II}(f)}}},} & (46)\end{matrix}$

where K_(V) may be the VCO constant. If the modulating noise mechanismis a combination of thermal and flicker noise, for f>0, S_(II)(f) may bewritten as:

$\begin{matrix}{{S_{II}(f)} = {\frac{A}{f} + N_{{Th}\; 1}}} & (47)\end{matrix}$

Therefore, the output phase noise only due to S_(II)(f) may equal:

$\begin{matrix}{{S_{\varphi\varphi}(f)} = {\frac{K_{V}^{2}A_{f}}{f^{3}} + \frac{K_{V}^{2}N_{{Th}\; 1}}{f^{2}}}} & (48)\end{matrix}$

If it were only due to the modulating mechanisms, the noise profile ofthe output would be indefinitely descending. However, there may bethermal noise sources that may not modulate the VCO, but may directlyappear at the output. An example of such a noise source may be thethermal noise of the series resistance of the inductor in an integratedVCO. This may not be noise in the phase but rather an additive amplitudenoise. However, the phase and amplitude noises may appear similarly in aPSD measurement on a spectrum analyzer. Therefore, for f>0 a term may beadded to the PSD to account for the thermal noise floor:

$\begin{matrix}{{S_{\varphi\varphi}(f)} = {\frac{K_{V}^{2}A_{f}}{f^{3}} + \frac{K_{V}^{2}N_{{Th}\; 1}}{f^{2}} + N_{{Th}\; 2}}} & (49)\end{matrix}$

Even though the AM and PM components may be indistinguishable in a PSD,there may be a difference between these components. The true PM noisethat is caused by the modulation of the VCO phase may create symmetricaland correlated sidebands, whereas the additive AM noise floor may not benecessarily correlated on the left and right sides of the carrier,unless it is converted to PM through hard-limiting, for example.Referring again to FIG. 19, in a typical VCO noise profile, the 1/f³ and1/f² areas on the left and right sides of the carrier may, therefore, becorrelated.

Although the thermal noise added, for example, by tank loss isuncorrelated with respect to the two sides of the carrier, it may stillbe possible to have correlated thermal noise sideband through othermechanisms.

FIG. 20 is a schematic block diagram of a voltage controlled oscillator(VCO) 2000 that may be utilized in accordance with an embodiment of theinvention. The VCO 2000 may comprise L-R-C circuits 2001 and 2002,transistors M1 and M2, and a grounded transistor M3. The cross-coupledtransistors M1 and M2 may provide a negative resistance that may cancelout the resonance tank loss lumped into resistors R. Transistor M3 mayprovide the bias current. The thermal noise of resistors R may directlyappear at the output and may be uncorrelated with respect to the sidesof the carrier.

During operation, transistors M1 and M2 may turn on and off in everycycle of oscillation. This action may alternate the bias current betweenthe two sides of the oscillator 2000 and may be similar to the mixingaction that may occur in an integrated mixer. The low frequency thermalnoise of M3 may be up-converted to around f₁, or the oscillationfrequency, and may create correlated sideband. Because of the parasiticcapacitance at node A, the thermal noise of M3 may have a finite cut-offfrequency that may or may not cause folding of the noise spectrum ontoitself. In any event, the sideband at the output due to the noise sourcemay be correlated. Thus, part of the thermal noise at the output comingfrom resistors R may be uncorrelated with respect to the left and rightsides of the carrier, while the part coming from transistor M3 may becorrelated in that regard. The thermal far-end noise of an integratedVCO, therefore, may be neither completely correlated nor uncorrelated.

Referring again to FIG. 18, if the output of a VCO is hard-limited, thenoise spectrum profile may be repeated at odd multiples of theoscillator frequency. The immediate vicinity of the f₁ oscillationfrequency, or the 1/f³ and 1/f² areas, may be correlated with respect tothe left and right sides of the carrier. At any odd multiple of f₁, thephase noise spectrum and its mirrored version may be folded onto eachother. The close-in phase noise and its mirrored version may, therefore,pass to the output with a gain of

$\left( \frac{2V_{m}}{\pi \; A_{1}} \right)^{2}$

and may add to each other. Because the two side bands are correlated,the result may be four times the power of one of them. In this way, theclose-in phase noise gain may be

$4{\left( \frac{2V_{m}}{\pi \; A_{1}} \right)^{2}.}$

The power at f₁ at the output may be

${P_{1}\left( \frac{4V_{m}}{\pi \; A_{1}} \right)}^{2},$

which may indicate that the gain for the carrier from input to theoutput may also equal

$4{\left( \frac{2V_{m}}{\pi \; A_{1}} \right)^{2}.}$

Therefore, the ratio of the carrier to sideband ratios may not changearound 1/f³ and 1/f². In addition, phase noise at the output may remainthe same as the input.

With regard to the thermal noise, it may depend on the level ofcorrelation of sidebands and its bandwidth. Depending on where the noisefloor is coming from, the thermal noise may start to fall off at somepoint. Even if the VCO noise profile extended to infinity, it may becomebandlimited upon entering the limiter because of the limited inputbandwidth of the limiter. The band limit may be M times the oscillationfrequency of the VCO, which means the thermal noise folds onto itself Mtimes. Therefore:

$\begin{matrix}{N_{Th} = {{4{N_{{Th}\; 1} \cdot \left( \frac{2V_{m}}{\pi \; A_{1}} \right)^{2}}} + {\left( {M - 2} \right){N_{{Th}\; 1} \cdot \left( \frac{2V_{m}}{\pi \; A_{1}} \right)^{2}}}}} & (50)\end{matrix}$

The first term on the right hand side of the equation comes from thefact that the correlated left and right sides, the sides close tocarrier, may fold on top of each other once. The (M−2) replicas thatfold back near the carrier may be uncorrelated. Equation (50) may besimplified to:

$\begin{matrix}{N_{Th} = {\left( {M + 2} \right){N_{{Th}\; 1} \cdot \left( \frac{2V_{m}}{\pi \; A_{1}} \right)^{2}}}} & (51)\end{matrix}$

For example, if M=2, the thermal noise may fold onto itself only twice,for correlated folding, and therefore the thermal noise floor may passthrough with a gain of

$4{\left( \frac{2V_{m}}{\pi \; A_{1}} \right)^{2}.}$

The far-end phase noise may also stay the same as the input. In thisway, if the noise profile has a larger bandwidth, more folding ofthermal noise may occur and the thermal noise level may relativelyincrease. In the general case of M>2, if the output signal of a VCO isapplied to a high gain limiter, the close-in phase noise at the outputof the limiter may remain the same, and the thermal noise floor mayincrease, depending on the effective bandwidth of the original noiseprofile.

In one aspect of the invention, a filter may be utilized in accordancewith a limiter in order to filter out phase noise prior to limiting thesignal and folding a phase noise harmonic on top of itself.

FIG. 21 is a schematic block diagram of a binary phase shift keying(PSK) modulator 2100 utilizing a limiter and a filter, in accordancewith an embodiment of the invention. Referring to FIG. 21, the PSKmodulator 2100 may comprise a phase detector 2101, a loop filter 2105, aVCO 2103, a frequency translation module 2107, and a modulation mixingmodule 2109.

The phase detector 2101 may comprise suitable logic, circuitry and/orcode and may be adapted to detect a phase and/or a frequency differencebetween a reference oscillation 2130 and a feedback oscillation 2132.The loop filter 2105 may be adapted to receive the difference signalfrom the phase detector 2101 and to convert it into a control signal2106. The VCO 2103 may receive the control signal 2106 and may produce amodulated output oscillation 2134 based on the control signal 2106.

The frequency translation module 2107 may comprise downconversion mixers2111 and 2113, and low pass filters 2115 and 2117. The downconversionmixer 2111 may be adapted to downconvert an in-phase component of thesignal 2136 received from the VCO 2103 by utilizing an in-phasecomponent of a local oscillation 2138. The downconversion mixer 2113 maybe adapted to downconvert a quadrature component of the signal 2136received from the VCO 2103 by utilizing a quadrature component of thelocal oscillation 2140.

During operation, the downconversion mixers 2111 and 2113 may generate adifference between the input signal 2136 and the local oscillatorsignals 2138 and 2140. The downconversion mixers 2111 and 2113, however,may also produce an additive frequency at their outputs, comprising theinput signal 2136 and the local oscillator signals 2138 and 2140,respectively. The low pass filters 2115 and 2117 may be adapted tofilter out the additive frequencies generated by the downconversionmixers 2111 and 2113.

The modulation mixing module 2109 may comprise modulation mixers 2119and 2121, a summing module 2123, a low pass filter 2125 and a limiter2127. The modulation mixer 2119 may be adapted to mix the in-phasecomponent of a modulating signal 2142 with the downconverted signalreceived from the output of the low pass filter 2115. The modulationmixer 2121 may be adapted to mix the quadrature component of amodulating signal 2144 with the downconverted signal received from theoutput of the low pass filter 2117. The resulting mixed signals may besummed by the summing module 2123 to produce a modulated signal 2146.The modulated signal 2146 may then be filtered by the low pass filter2125. The filtered signal may be limited by the limiter 2127 to producethe feedback signal 2132. The feedback signal 2132 may in turn becompared to the reference signal 2130 by the phase detector 2101.

In another aspect of the invention, the PSK modulator 2100 may comprisea processor 2126. The processor 2126 may comprise on-chip processor andmay be configured to analyze spectral content of noise profile. Inoperation, the processor 2126 may be coupled to the output of thesumming module 2123 and to the low-pass filter 2125. The processor mayanalyze the spectral content of the modulated signal 2146 and maydetermine filter characteristics, such as filter coefficients, for thelow-pass filter 2125. In this way, the processor 2126 may configure thelow-pass filter 2125 so that the low-pass filter may filter out one ormore noise harmonics and avoid folding of those harmonics in the outputsignal after the limiter 2127.

The processor 2126 may also be a part of a portable analyzing deviceutilizing spectral analysis hardware, firmware and/or software, forexample.

In a locked state, the signal output 2134 of the binary PSK modulator2100 may be calculated as f_(out)=f_(RF)±f_(BB). If bit ‘1’ isconstantly being transmitted, or f_(out)=f_(RF)+f_(BB), the highfrequency modulated signal 2134 may be down converted through mixingwith f_(LO)>f_(RF), utilizing the in-phase and quadrature components Iand Q, respectively. At the output of this mixer, both downconverted(f_(LO)−f_(out)) and upconverted (f_(LO)+f_(out)) signals may exist. Thelow pass filter LPF1 2115 may be primarily used to reject theupconverted (f_(LO)+f_(out)) signals. The baseband modulation may bemixed with the downconverted signal in the I and Q paths and summed bythe summing module 2123. At point X, f_(LO)−f_(out)−f_(BB)=f_(LO)−f_(RF)may be obtained. The resulting signal 2146, after being filtered by thelow-pass filter 2125 and limited by the limiter 2127, may be comparedagainst a reference signal 2130 to generate the control signal 2106 forthe VCO 2103. Prior to entering the phase detector 2101, the modulatedsignal 2146 may be hard-limited by the limiter 2127 to provide arail-to-rail digital signal.

In a different aspect of the invention, the low pass filter 2125 may beselected with different filtering parameters to filter different phasenoise characteristics within the modulated signal 2146.

Certain specification may also be met on the level of allowable spurioussignal in the adjacent channel within the modulated signal 2146. Forinstance, at 3 f_(BB) away from f_(RF), the spur may be 60 dB down.

FIG. 22 is a graphical representation 2200 of an exemplary signal noisecharacteristic for a limited signal with filtration, in accordance withan embodiment of the invention. In one aspect of the invention, it maybe assumed that f_(REF)=50 MHz, f_(BB)=1 MHz, f_(LO)=550 MHz andf_(RF)=500 MHz. Referring again to FIG. 21, if bit “1” is beingtransmitted, f_(out)=551 MHz and f_(LO)−f_(out)=51 MHz. Thedownconversion mixers 2111 and 2113 may not be ideal and may addharmonics to both the input signal 2136 and the local oscillator signals2138 and 2140. Therefore, the modulated signal 2146 at point X may alsohave energy around 3(f_(LO)−f_(out))=153 MHz, which may not be filteredby the low pass filters 2115 and 2117. The downconverted signal may bemixed by the mixers 2119 and 2121 with f_(BB) to produce 51MHz−f_(BB)=50 MHz.

Referring to FIG. 22, it may be illustrated that because of thenonlinearity of the modulation mixers 2119 and 2121, the spectrum mayalso reproduce energy at 51 MHz+3 f_(BB)=54 MHz. In this way, by pushingthe nonlinearity below a minimum, the energy at 54 MHz may be reduced,and hence the adjacent channel specification may be met. However, the153 MHz component from the output of the downconversion mixers may alsobe mixed with f_(BB) in the modulation mixers and may produce spikes at153 MHz+f_(BB)=154 MHz and 153 MHz−3 f_(BB)=150 MHz, as illustrated onFIG. 22. If the effect of the limiter is ignored, the energy at around150 MHz may be eventually filtered out by the loop filter 2105 in FIG.21. Since the spike at 53 MHz is considerably low, the 3 MHz spec may besatisfied. Nonetheless, utilizing the results of the previous section,and by employing a unity gain limiter for simplicity, the 153 MHz spikemay fold onto both 53 MHz and 47 MHz points with a gain of 0.5.

Therefore, on top of the existing signal at 53 MHz, there may also be astrong component at that frequency with a magnitude of −59 dBV, whichmay be 17 dB below the desired channel. By utilizing a low pass filter,the 153 MHz signal may be attenuated by at least 43 dB prior to thelimiting action.

FIG. 23 is a graphical representation 2300 of an exemplary signal noisecharacteristic for a limited signal without filtration, in accordancewith an embodiment of the invention. Referring to FIG. 23, the graphicalrepresentation 2300 may illustrate the simulation results for a signalafter a limiter without the use of a low pass filter prior to thelimiting action.

FIG. 24 is a flow diagram of an exemplary method 2400 for processing asinusoidal wave signal with a phase noise profile, in accordance with anembodiment of the invention. At step 2401, an output signal may beobtained from a VCO. At step 2403, in-phase and quadrature components ofthe output signal may be downconverted utilizing mixers and a localoscillator signal, for example. The in-phase component of the outputsignal may be downconverted utilizing the in-phase component of a localoscillator signal. Similarly, the quadrature component of the outputsignal may be downconverted utilizing the quadrature component of thelocal oscillator signal.

At step 2405, an upconversion frequency at the output of thedownconversion mixers may be filtered out so that the frequencyrepresenting a difference between the local oscillator frequency and theinput frequency may remain. At step 2407, the in-phase and quadraturecomponents may be modulated with a modulation signal within modulationmixers, for example. At step 2409, the modulated in-phase and quadraturecomponents may be added to obtain a modulated signal. At step 2411,spectral content of the noise profile of the modulated signal may beanalyzed. For example, an on-chip processor, or a removable device, maybe utilized to analyze the spectral content. At step 2411, the modulatedsignal may be low-pass filtered to remove phase noise characteristics,prior to the signal being limited. The spectral content analysis may beutilized to determine one or more filter coefficients which configurethe low-pass filter. At step 2413, the filtered modulated signal may belimited by a limiter.

While the invention contemplates the application of a filter inaccordance with a limiter within a binary PSK modulator, or aphase-locked loop, the invention is not limited in this way. A filter inaccordance with a limiter may also be applied to other circuits orarrangements so that a phase-noise profile of a signal may be reducedprior to the signal being limited by the limiter.

Accordingly, aspects of the invention may be realized in hardware,software, firmware or a combination thereof. The invention may berealized in a centralized fashion in at least one computer system, or ina distributed fashion where different elements are spread across severalinterconnected computer systems. Any kind of computer system or otherapparatus adapted for carrying out the methods described herein issuited. A typical combination of hardware, software and firmware may bea general-purpose computer system with a computer program that, whenbeing loaded and executed, controls the computer system such that itcarries out the methods described herein.

The invention may also be embedded in a computer program product, whichcomprises all the features enabling the implementation of the methodsdescribed herein, and which when loaded in a computer system is able tocarry out these methods. Computer program in the present context maymean, for example, any expression, in any language, code or notation, ofa set of instructions intended to cause a system having an informationprocessing capability to perform a particular function either directlyor after either or both of the following: a) conversion to anotherlanguage, code or notation; b) reproduction in a different materialform. However, other meanings of computer program within theunderstanding of those skilled in the art are also contemplated by thepresent invention.

While the invention has been described with reference to certainembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted withoutdeparting from the scope of the present invention. In addition, manymodifications may be made to adapt a particular situation or material tothe teachings of the present invention without departing from its scope.Therefore, it is intended that the present invention not be limited tothe particular embodiments disclosed, but that the present inventionwill include all embodiments falling within the scope of the appendedclaims.

1-32. (canceled)
 33. A method for processing a signal with acorresponding noise profile, the method comprising: analyzing spectralcontent of the noise profile; filtering at least one noise harmonicwithin the signal based on said analyzed spectral content; and limitingsaid filtered signal.
 34. The method according to claim 33, wherein thenoise profile comprises a phase noise profile.
 35. The method accordingto claim 33, wherein the signal comprises at least one of a sinusoidalsignal and a noise signal.
 36. The method according to claim 33,comprising determining at least one filter coefficient that is used tofilter said at least one noise harmonic.
 37. The method according toclaim 33, wherein said filtering comprises low pass filtering.
 38. Themethod according to claim 33, wherein said limiting compriseshard-limiting said filtered signal.
 39. The method according to claim33, comprising detecting a phase difference between said limited signaland a reference signal.
 40. A system for processing a signal with acorresponding noise profile, the system comprising: a processor thatanalyzes spectral content of the noise profile; a filter that filters atleast one noise harmonic within the signal based on said analyzedspectral content; and a limiter that limits said filtered signal. 41.The system according to claim 40, wherein the noise profile comprises aphase noise profile.
 42. The system according to claim 40, wherein thesignal comprises at least one of a sinusoidal signal and a noise signal.43. The system according to claim 40, wherein the processor determinesat least one filter coefficient that is used to filter said at least onenoise harmonic.
 44. The system according to claim 40, wherein saidfilter comprises a low-pass filter.
 45. The system according to claim40, wherein said limiter comprises a hard-limiter that limits saidfiltered signal.
 46. The system according to claim 40, comprising aphase detector that detects a phase difference between said limitedsignal and a reference signal.
 47. A method for processing a signal witha corresponding noise profile, the method comprising: analyzing spectralcontent of the noise profile; modulating the signal; filtering at leastone noise harmonic within the modulated signal based on said analyzedspectral content; and limiting said filtered signal.
 48. The methodaccording to claim 47, comprising downconverting the signal prior tosaid modulating.
 49. The method according to claim 48, comprisingdownconverting at least one signal component of the signal.
 50. Themethod according to claim 49, wherein said at least one signal componentof the signal comprises one or both of an in-phase signal component anda quadrature signal component.
 51. The method according to claim 48,comprising mixing said downconverted signal with a local oscillatorsignal.
 52. The method according to claim 51, comprising filtering saidmixed signal.
 53. The method according to claim 52, wherein saidfiltering comprises low pass filtering of a sum of a carrier frequencyof the signal and a reference frequency of said local oscillator signal.54. The method according to claim 50, comprising modulating saidin-phase signal component and said quadrature signal component with amodulation frequency.
 55. The method according to claim 54, comprisingadding said modulated in-phase signal component and said modulatedquadrature signal component to obtain a downconverted modulated signal.56. A system for processing a signal with a corresponding noise profile,the system comprising: a processor that analyzes spectral content of thenoise profile; a modulator that modulates the signal; a filter thatfilters at least one noise harmonic within the signal based on saidanalyzed spectral content; and a limiter that limits said filteredsignal.
 57. The system according to claim 56, comprising a downconverterthat downconverts the signal prior to said modulating.
 58. The systemaccording to claim 57, wherein said downconverter downconverts at leastone signal component of the signal.
 59. The system according to claim58, wherein said at least one signal component of the signal comprisesone or both of an in-phase signal component and a quadrature signalcomponent.
 60. The system according to claim 57, comprising a mixer thatmixes said downconverted signal with a local oscillator signal.
 61. Thesystem according to claim 60, comprising a filter that filters saidmixed signal.
 62. The system according to claim 61, wherein said filtercomprises a low pass filter that filters a sum of a carrier frequency ofthe signal and a reference frequency of said local oscillator signal.63. The system according to claim 59, comprising a modulation mixer thatmodulates said in-phase signal component and said quadrature signalcomponent with a modulation frequency.
 64. A system for processing asignal with a corresponding noise profile, the system comprising: atleast one processor that analyzes spectral content of the noise profile;said at least one processor modulates the signal; said at least oneprocessor filters at least one noise harmonic within the signal based onsaid analyzed spectral content; and said at least one processor limitssaid filtered signal.
 65. The system according to claim 64, wherein saidat least one processor downconverts the signal prior to said modulating.66. The system according to claim 65, wherein said at least oneprocessor downconverts at least one signal component of the signal. 67.The system according to claim 66, wherein said at least one signalcomponent of the signal comprises one or both of an in-phase signalcomponent and a quadrature signal component.
 68. The system according toclaim 65, wherein said at least one processor mixes said downconvertedsignal with a local oscillator signal.
 69. The system according to claim68, wherein said at least one processor filters said mixed signal. 70.The system according to claim 69, wherein said at least one processorfilters a sum of a carrier frequency of the signal and a referencefrequency of said local oscillator signal.
 71. The system according toclaim 67, wherein said at least one processor modulates said in-phasesignal component and said quadrature signal component with a modulationfrequency.